Let's keep our thinking caps on, you know that's a ludicrously inaccurate claim.
It's not just a probable physical impossibility, it's a certain technical impossibility to summit Everest with an animal in tow.
Were Rupee not born at 11,000 ft. I'd even consider it a risky move to bring him on the multi-day acclimatization trek up to Base Camp (~17500 ft.) which is what actually happened (don't know where that pic was taken, could be anywhere up there).
I hope in his travels he never experienced altitude sickness, it's hard enough to keep ahead of in a victim who can speak... and you'd be first in line condemning the stunt had anything gone wrong.